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**Heat Transfer Modeling**

Headlamp modelled with Discrete Ordinates Radiation Model

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**Outline Introduction Conjugate Heat Transfer Natural Convection**

Radiation Periodic Heat Transfer

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**Introduction Energy transport equation:**

Energy source due to chemical reaction is included for reacting flows. Energy source due to species diffusion included for multiple species flows. Always included in coupled solver; can be disabled in segregated solver. Energy source due to viscous heating: Describes thermal energy created by viscous shear in the flow. Important when shear stress in fluid is large (e.g., lubrication) and/or in high-velocity, compressible flows. Often negligible not included by default for segregated solver; always included for coupled solver. In solid regions, simple conduction equation solved. Convective term can also be included for moving solids.

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**Conjugate Heat Transfer**

Ability to compute conduction of heat through solids, coupled with convective heat transfer in fluid. Coupled Boundary Condition: available to wall zone that separates two cell zones. Grid Velocity vectors Temperature contours Example: Cooling flow over fuel rods

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**Natural Convection - Introduction**

Natural convection occurs when heat is added to fluid and fluid density varies with temperature. Flow is induced by force of gravity acting on density variation. When gravity term is included, pressure gradient and body force term in momentum equation is written as: This format avoids potential roundoff error when gravitational body force term is included. where

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**Natural Convection - Boussinesq Model**

Makes simplifying assumption that density is uniform. Except for body force term in momentum equation, which is replaced by: Valid when density variations are small (i.e., small variations in T). Provides faster convergence for many natural-convection flows than by using fluid density as function of temperature. Constant density assumptions reduces non-linearity. Use when density variations are small. Cannot be used with species calculations or reacting flows. Natural convection problems inside closed domains: For steady-state solver, Boussinesq model must be used. Constant density, o, allows mass in volume to be defined. For unsteady solver, Boussinesq model or Ideal gas law can be used. Initial conditions define mass in volume.

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**User Inputs for Natural Convection**

1. Set gravitational acceleration. Define Operating Conditions... 2. Define density model. If using Boussinesq model: Select boussinesq as the Density method and assign constant value, o. Define Materials... Set Thermal Expansion Coefficient, . Set Operating Temperature, To. If using temperature dependent model, (e.g., ideal gas or polynomial): Specify Operating Density or, Allow Fluent to calculate o from a cell average (default, every iteration).

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Radiation Radiation effects should be accounted for when is of equal or greater magnitude than that of convective and conductive heat transfer rates. To account for radiation, radiative intensity transport equations (RTEs) are solved. Local absorption by fluid and at boundaries links RTEs with energy equation. Radiation intensity, I(r,s), is directionally and spatially dependent. Intensity, I(r,s), along any direction can be modified by: Local absorption Out-scattering (scattering away from the direction) Local emission In-scattering (scattering into the direction) Five radiation models are provided: Discrete Ordinates Model (DOM) Discrete Transfer Radiation Model (DTRM) P-1 Radiation Model Rosseland Model Surface-to-Surface (S2S)

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**Discrete Ordinates Model**

The radiative transfer equation is solved for a discrete number of finite solid angles, si: Advantages: Conservative method leads to heat balance for coarse discretization. Accuracy can be increased by using a finer discretization. Most comprehensive radiation model: Accounts for scattering, semi-transparent media, specular surfaces, and wavelength-dependent transmission using banded-gray option. Limitations: Solving a problem with a large number of ordinates is CPU-intensive. absorption emission scattering

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**Discrete Transfer Radiation Model (DTRM)**

Main assumption: radiation leaving surface element in a specific range of solid angles can be approximated by a single ray. Uses ray-tracing technique to integrate radiant intensity along each ray: Advantages: Relatively simple model. Can increase accuracy by increasing number of rays. Applies to wide range of optical thicknesses. Limitations: Assumes all surfaces are diffuse. Effect of scattering not included. Solving a problem with a large number of rays is CPU-intensive.

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P-1 Model Main assumption: Directional dependence in RTE is integrated out, resulting in a diffusion equation for incident radiation. Advantages: Radiative transfer equation easy to solve with little CPU demand. Includes effect of scattering. Effects of particles, droplets, and soot can be included. Works reasonably well for combustion applications where optical thickness is large. Limitations: Assumes all surfaces are diffuse. May result in loss of accuracy, depending on complexity of geometry, if optical thickness is small. Tends to overpredict radiative fluxes from localized heat sources or sinks.

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**Surface-to-Surface Radiation Model**

The S2S radiation model can be used for modeling enclosure radiative transfer without participating media. e.g., spacecraft heat rejection system, solar collector systems, radiative space heaters, and automotive underhood cooling View-factor based model Non-participating media assumed. Limitations: The S2S model assumes that all surfaces are diffuse. The implementation assumes gray radiation. Storage and memory requirements increase very rapidly as the number of surface faces increases. Memory requirements can be reduced by using clusters of surface faces. Clustering does not work with sliding meshes or hanging nodes. Cannot be used with periodic or symmetry boundary conditions.

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**Choosing a Radiation Model**

For certain problems, one radiation model may be more appropriate in general. Define Models Radiation... Computational effort: P-1 gives reasonable accuracy with less effort. Accuracy: DTRM and DOM more accurate. Optical thickness: DTRM/DOM for optically thin media (optical thickness << 1); P-1 better for optically thick media. Scattering: P-1 and DOM account for scattering. Particulate effects: P-1 and DOM account for radiation exchange between gas and particulates. Localized heat sources: DTRM/DOM with sufficiently large number of rays/ ordinates is more appropriate.

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**Periodic Heat Transfer (1)**

Also known as streamwise-periodic or fully-developed flow. Used when flow and heat transfer patterns are repeated, e.g., Compact heat exchangers Flow across tube banks Geometry and boundary conditions repeat in streamwise direction. inflow outflow Outflow at one periodic boundary is inflow at the other

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**Periodic Heat Transfer (2)**

Temperature (and pressure) vary in streamwise direction. Scaled temperature (and periodic pressure) is same at periodic boundaries. For fixed wall temperature problems, scaled temperature defined as: Tb = suitably defined bulk temperature Can also model flows with specified wall heat flux.

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**Periodic Heat Transfer (3)**

Periodic heat transfer is subject to the following constraints: Either constant temperature or fixed flux bounds. Conducting regions cannot straddle periodic plane. Thermodynamic and transport properties cannot be functions of temperature. Viscous heating and volumetric heat sources cannot be used with constant wall temperature boundary conditions. Contours of Scaled Temperature

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**Summary Heat transfer modeling is available in all Fluent solvers.**

After activating heat transfer, you must provide: Thermal conditions at walls and flow boundaries Fluid properties for energy equation Available heat transfer modeling options include: Species diffusion heat source Combustion heat source Conjugate heat transfer Natural convection Radiation Periodic heat transfer

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